Duplicating an object while perfectly aligning each edge
So many ways, depending ..

Assuming this is in Edit mode, and these are one-off parts already measured to fit a hole in the existing mesh, aligned to the world as shown, you could:


Set Snap to 'Vertex, Active'
Select the whole part, and in Vertex Mode, make one of its bottom right vertices active
ShiftDX duplicate the part, snapping the rear vertex of the duplicated part to the corresponding front vertex of the existing one
ShiftR repeat the operation until the hole is filled
With all selected, AltM > 'By Distance' merge coincident vertices.


BUT.. this whole process seems a bit topsy-turvy, since you would already have had to measure up the part, somehow? Going back a couple of steps..




In Edge Mode, Right-click > 'Subdivide' the opposing edges, adjust the cuts to 4
I inset the five new faces, with the tool set to 'Individual' and 'Depth' adjusted to raise the inset faces to the desired distance
Make tweaks afterwards?


If you had hundreds to do, or reasons to do this non-destructively, you could temporarily split the part off into a new object, and use an Array modifier, before rejoining into one object..